What is the role of elasticity in space-time according to Sakharov's theory?

[Fuzzy Logic]

If gravity distorts space-time, does space-time return to equilibrium when the gravity mass is gone (let's say it vanished instantly)? If so, what happens to other satellite masses that are caught in the same gravity well?

Does space-time just instantly slip out from under them? Or do the satellites get dragged along with it?

 

[Nabeshin]

If gravity distorts space-time, does space-time return to equilibrium when the gravity mass is gone (let's say it vanished instantly)? If so, what happens to other satellite masses that are caught in the same gravity well?

Does space-time just instantly slip out from under them? Or do the satellites get dragged along with it?

In general, yes the spacetime will return to the background minkowski (read: flat) configuration when the mass is gone. However, gravitational waves can leave an 'imprint' on spacetime even after they have passed through a region, permanently altering the spacetime geometry. Look up gravitational wave memory.

 

[Antientrophy]

Space is definitely elastic and flexible. If it wasn't the universe would have shattered into an infinite amount pieces a long time ago.

 

[Chronos]

Space is not a 'substance', so it has no properties such as elasticity. Gravity affects 'things' that pass through the gravitational field - like matter and photons - altering their path. Some would say the gravitational field IS the fabric of space. Some would even say that if gravity suddenly disappeared, so would space.
re: http://www.astronomycafe.net/gravity/gravity.html

"Perhaps the most unusual thing about gravity we know about is that, unlike the other forces of nature, gravity is intimately related to space and time. In fact, space and time are viewed by physicists, and the mathematics of relativity theory, as qualities of the gravitational field of the cosmos that have no independent existence. Gravity does not exist like the frosting on a cake, embedded in some larger arena of space and time. Instead, the 'frosting' is everything, and matter is embedded and intimately and indivisibly connected to it. If you could turn off gravity, it is mathematically predicted that space and time would also vanish!"

 

[kirtg]

If spacetime is not a substance, where do virtual particles come from?

 

[Helios]

Sakharov ( 1967 ) suggested accounting for the effects of general relativity by introducing the concept of an "elasticity of space," analogous to the well-known curvature of space-time.